Pith Number

pith:6YOVRIHI

pith:2012:6YOVRIHIVNK33CVJYS5AIN3ZUA

not attested not anchored not stored refs pending

The spherical Hall algebra of Spec(Z)

Eric Vasserot, Mikhail Kapranov, Olivier Schiffmann

arxiv:1202.4073 v1 · 2012-02-18 · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6YOVRIHIVNK33CVJYS5AIN3ZUA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:02:01.420627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f61d58a0e8ab55bd8aa9c4ba043779a036569a56d0c04d4292b3a28ce0c02e93

Aliases

arxiv: 1202.4073 · arxiv_version: 1202.4073v1 · doi: 10.48550/arxiv.1202.4073 · pith_short_12: 6YOVRIHIVNK3 · pith_short_16: 6YOVRIHIVNK33CVJ · pith_short_8: 6YOVRIHI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6YOVRIHIVNK33CVJYS5AIN3ZUA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f61d58a0e8ab55bd8aa9c4ba043779a036569a56d0c04d4292b3a28ce0c02e93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd869cd506bc3ba75ab6999aa57acc0d1381d52c3851472abb2ecd197cb9092d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-02-18T11:54:46Z",
    "title_canon_sha256": "119424af493cfc397d75cfe4e099f6b8478396f6d95b914ff6184bc260863bf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4073",
    "kind": "arxiv",
    "version": 1
  }
}